Coherent state quantization of angle, time, and more irregular functions and distributions

TL;DR

This paper demonstrates that coherent state quantization can be extended to irregular classical observables and distributions, allowing for their quantum counterparts beyond smooth functions.

Contribution

It introduces a method to quantize irregular functions and distributions using coherent states, expanding the scope of quantization techniques.

Findings

Quantum versions of irregular observables are constructed.

Coherent state quantization applies to tempered distributions.

The approach broadens the class of classical functions that can be quantized.

Abstract

The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of irregular observables living on the classical phase space, such as the angle function, the time function of a free particle and even a large set of distributions comprising the tempered distributions.